Sorry I didn't get back to this thread, had some stuff going on.
The FCM supplies a pulse of a bit higher voltage to pull the clutch coil in, then backs off to around 8v or so to hold it on. It takes more "oomph" to move the plate initially, but less to keep it there.
So that is why you see a pulsing on a test light. Test lights are not a good way to test this type of circuit because of this.
KOEO, if you press the A/C button (with the blower turned on...any speed) the cooling fans should both come on low speed.
Even if your fans were both dead, the compressor would still come on with the engine running and the A/C button pressed. It just won't STAY engaged, because as soon as the refrigerant pressure sensor goes too high, the FCM will turn off the compressor.
While the G/J sometimes have control heads that go bad, the NBs are FAR worse about it for some reason, even though they are wired pretty much the same way. The NBs are also FAR worse for the ignition switch connector shell getting hot and cooking, causing all sorts of electrical problems.
You can watch the A/C request in the Engine data, I forget which Measuring Group, but it is in there. That is an easy way to make sure the button's signal is getting to the ECU. Ultimately the ECU has say on compressor engagement. It will not allow the clutch to engage if: the engine is not running (no tach signal), the coolant is too high (overheating, CTS signal), full power is requested (RPM/pedal position, etc.). But this is done via a signal to the FCM, as the FCM is actually what controls the clutch power. It just does so with the ECU's permission.